A fall nor’easter dropped more than three inches of snow on parts of Central and Southeastern Massachusetts on Wednesday night, with some areas seeing more than five inches, according to the National Weather Service.

A mixture of snow and freezing rain was expected to continue in most areas after midnight, the weather service said, with more rain forecast for Thursday before giving way to sunnier weather heading into the weekend. The stormy conditions Wednesday led to traffic accidents, power outages, and wind damage to trees and wires.

“We are expecting some more snowfall overnight,” said Matt Doody, a weather service meteorologist, in a phone interview late Wednesday. “Now, granted the bulk of the snowfall has probably already fallen, but there will still be a little more.”

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By late Wednesday night, reported snowfall totals stood at 3 inches in Seekonk, 4 inches in Shrewsbury, 5 inches in Southbridge, and 5.6 inches in Foxborough, according to the weather service.

Overnight accumulation was forecast at 1 to 5 inches in the eastern part of the state, and 2 to 6 inches in Central and Western Massachusetts, according to a weather service advisory posted Wednesday night.

Doody said late Wednesday that the weather service had extended its winter weather advisory to virtually the entire state, except for the Cape and Islands. Such an advisory is issued when snow or ice is expected to develop.

“Any snow or ice would make driving and walking difficult” on untreated roads, the advisory said.

High winds also battered the state on Wednesday, according to the weather service.

By late afternoon, the service had received reports of winds bringing down trees and wires in a number of communities, including Plymouth, Duxbury, Fairhaven, Needham, Worcester, Natick, and Taunton.

At 6 p.m., police closed the stretch of Route 3A that passes Plymouth Beach because of high surf and a storm surge that had propelled ocean water over a 6-foot sea wall and across the highway. A steady wind of 30 miles per hour with gusts up to 50 miles per hour tossed up 4-to-6-foot waves in Plymouth Harbor that easily breached the breakwater protecting fishing boats in the inner harbor.

Later in the evening, peak wind gusts of over 60 mph were reported in Plymouth, Nantucket, Martha’s Vineyard, and Fairhaven, according to the weather service.

Gusts in the high 50s were reported on parts of the Cape and in Duxbury, and a 76-mph gust was reported off Cuttyhunk Island, south of New Bedford.

In addition to Plymouth, the fierce winds also brought coastal flooding to Nantucket, Chatham, and Quincy, the weather service said.

National Grid reported at about 10:30 p.m. that approximately 1,599 customers were without power in the state, mostly in the southeastern region, while NStar reported 3,089 customers without power, mostly on the south coast and the Cape and Islands.